Testing Evidence Accrual Models by Manipulating Stimulus Onset

Abstract

Many models of response time assume that subjects accrue stimulus “evidence” samples in time (e.g., random walk models, counter models). In this paper, the concept of one stimulus dominating another is used to construct a test of the whole class of evidence accrual models. For an example of dominance, consider stimuli that are presented either virtually instantaneously (stepped) or in a gradually increasing manner (ramped). Ramped stimuli are presented such that the ramped portion precedes the stepped onset of stepped stimuli. In this case ramped stimuli dominate stepped stimuli. In this paper the class of evidence accrual models is formalized. It is shown that under appropriate assumptions evidence accrual models do predict more accurate responses to dominating stimuli. However, this result does not hold for response latencies. There are anomalous cases where an evidence accrual model (the accumulator model of Vickers (1970, Ergonomics13, 37–58)) predicts slower mean correct response latencies to dominating stimuli. It is shown through extensive computer simulation that these anomalous cases occur only when response criteria are so asymmetric that there are exceedingly extreme response biases. For experiments where response biases are not exceedingly extreme, random walk and accumulator models predict more accurate and quicker correct responses to dominating stimuli. In sum, manipulating the time course of stimuli in accordance with the concept of dominance can provide empirical tests of the class of evidence accrual models.